Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 146, pp. 1-14.

Title: Resolvent estimates for scalar fields with electromagnetic perturbation

Author: Mirko Tarulli (Univ. di Pisa, Italy)

Abstract: 
  In this note we prove some estimates for the resolvent of the
  operator $-\Delta$ perturbed by the differential operator
  $$
  V(x,D)=ia(x)\cdot \nabla+V(x)\quad \mbox{in }\mathbb{R}^3\,.
  $$
  This differential operator is of short range type
  and a compact perturbation  of the Laplacian on $\mathbb{R}^3$.
  Also we find estimates in the space-time norm for the solution
  of the wave equation  with such  perturbation.

Submitted July 12, 2004. Published December 7, 2004.
Math Subject Classifications: 35L05, 35J10, 35P25, 35B25, 35B34, 35B40.
Key Words: Perturbed wave equation; perturbed Schrodinger equation;
     perturbed Dirac equation; resolvent; short range perturbation;
     smoothing estimates.